The concept of average depth for bottom time portion of the dive, and using that depth to determine the deco schedule (or NDL for that matter) using tables is not at all radical. If you think it is crazy snake oil, could you please humour me and test using your preferred deco planner tool and settings (my choice is Subsurface with Bühlmann gf 60/85 but that's just me)
A) Square profile of any depth, bottom time (e.g. 4min to descend to 50m, leave bottom at 30min runtime, using 18/45 bottom gas and 50% deco gas, Subsurface tells me I get out of the water at 76min)
B) A deep-to-shallow profile of same average bottom depth and time (e.g. 4min to descend to 60m, stay for 10min, ascend to 40m over 6min, stay for 10min, leave bottom at 30min runtime, same gassed as above. I get out of the water at 72min - 4min less deco than square profile A)
C) A shallow-to-deep profile "reverse of above" (e.g. 4min to descend to 40m, stay for 10min, descend to 60m over 6min, stay for 10min, leave bottom at 30min. I get out of the water at 80min - 4min more deco than square profile A)
D) A sawtooth profile of same average depth and bottom time (e.g. drop to 60m over 4min, ascend to 40m over 7min, back to 60m over 7min, back to 40m over 7m, descend to 50m over 5min, leave bottom at 30min. I get out of the water at 75min - just 1min less than square profile A).
Let me guess. Whatever you chose, case B (deep to shallow) required a bit less deco than case A (square), case C (shallow to deep) required a bit more deco, and case D (sawtooth) required about the same deco as case A.
You can use maths to prove that assuming exponential decay of gas absorption for tissues with a certain half-time that deep to shallow will always end up with less inert gas absorption than a square profile, and shallow to deep will absorb more.
So what? The upshot is that for a deep to shallow profile (most common for multi-level dives) you can safely assume it is similar to a square profile of same average depth and bottom time. You'll take a little bit more time doing deco than an optimized plan, but it will work. You should avoid (or otherwise compensate) shallow to deep profiles when using depth averaging. There are other issues with sawtooth profiles not covered by Bühlmann or VPM models, but they are inevitable in many caves and some wrecks, and consensus seems to be that they are ok if the sawtoothing is not too rapid.
There are pseudo-averaging techniques that attempt to compensate in the deep-to-shallow vs shallow-to-deep bias.
Of course, planning based on an accurate profile will give a more accurate deco schedule, and should be done where feasible. Computer can/should be relied upon too. But averaging can be useful too either as a backup, or in anticipating changes to what deco will be required during a dive.